A random sample ofn₁=20winter days in Denver gave a sample mean pollution indexx₁=43. Previous studies show that₁=11. For Englewood (a suburb of Denver), a random sample ofn₂=12winter days gave a sample mean pollution index ofx₂=36. Previous studies show that₂=13. Assume the pollution index is normally distributed in both Englewood and Denver. Do these data indicate that the mean population pollution index of Englewood is different (either way) from that of Denver in the winter? Use a 1% level of significance.

What is the value of the sample test statistic? (Test the difference₁₂. Round your answer to two decimal places.)

(c)

Find (or estimate) theP-value. (Round your answer to four decimal places.)

Q2

A Michigan study concerning preference for outdoor activities used a questionnaire with a six-point Likert-type response in which 1 designated "not important" and 6 designated "extremely important." A random sample ofn₁=48adults were asked about fishing as an outdoor activity. The mean response wasx₁=4.9. Another random sample ofn₂=50adults were asked about camping as an outdoor activity. For this group, the mean response wasx₂=5.5. From previous studies, it is known that₁=1.5and₂=1.2. Does this indicate a difference (either way) regarding preference for camping versus preference for fishing as an outdoor activity? Use a 5% level of significance.

Note: A Likert scale usually has to do with approval of or agreement with a statement in a questionnaire. For example, respondents are asked to indicate whether they "strongly agree," "agree," "disagree," or "strongly disagree" with the statement.

a) What is the value of the sample test statistic? (Test the difference₁₂. Round your answer to two decimal places.)

b) Find (or estimate) theP-value. (Round your answer to four decimal places.)

Q3

A random sample ofn₁= 10 regions in New England gave the following violent crime rates (per million population).

x₁:New England Crime Rate3.53.94.24.13.34.11.84.82.93.1

Another random sample ofn₂= 12 regions in the Rocky Mountain states gave the following violent crime rates (per million population).

x₂:Rocky Mountain Crime Rate3.74.14.75.53.34.83.52.43.13.55.22.8

Assume that the crime rate distribution is approximately normal in both regions.

(a)

Use a calculator to calculatex₁,s₁,x₂, ands₂. (Round your answers to four decimal places.)

x₁=

s₁=

x₂=

s₂=

What is the value of the sample test statistic? (Test the difference₁₂. Round your answer to three decimal places.)

Q4

In this problem, assume that the distribution of differences is approximately normal.Note: For degrees of freedomd.f. not in the Student'sttable, use the closestd.f. that issmaller. In some situations, this choice ofd.f. may increase theP-value by a small amount and therefore produce a slightly more "conservative" answer.

Are America's top chief executive officers (CEOs) really worth all that money? One way to answer this question is to look at rowB, the annual company percentage increase in revenue, versus rowA, the CEO's annual percentage salary increase in that same company. Suppose a random sample of companies yielded the following data:

B: Percent increase for company

24 25 25 18 6 4 21 37

A: Percent increase for CEO

21 23 24 14 4 19 15 30

Do these data indicate that the population mean percentage increase in corporate revenue (rowB) is different from the population mean percentage increase in CEO salary? Use a 5% level of significance. (Letd=BA.)

What is the value of the sample test statistic? (Round your answer to three decimal places.)

Q5

In this problem, assume that the distribution of differences is approximately normal.Note: For degrees of freedomd.f. not in the Student'sttable, use the closestd.f. that issmaller. In some situations, this choice ofd.f. may increase theP-value by a small amount and therefore produce a slightly more "conservative" answer.

At five weather stations on Trail Ridge Road in Rocky Mountain National Park, the peak wind gusts (in miles per hour) for January and April are recorded below.

Weather Station 1 2 3 4 5

January. 135 120 126 64 78

April 108 115 100 88 61

Does this information indicate that the peak wind gusts are higher in January than in April? Use= 0.01. (Letd= JanuaryApril.)

What is the value of the sample test statistic? (Round your answer to three decimal places.)

Q6

In this problem, assume that the distribution of differences is approximately normal.Note: For degrees of freedom d.f. not in the Student'st-table, use the closest d.f. that issmaller. In some situations, this choice of d.f. may increase theP-value by a small amount and therefore produce a slightly more "conservative" answer.

In environmental studies, sex ratios are of great importance. Wolf society, packs, and ecology have been studied extensively at different locations in the U.S. and foreign countries. Sex ratios for eight study sites in northern Europe are shown below.

Location of Wolf Pack%

Males (Winter)% Males (Summer)

Finland76 57

Finland51 54

Finland71 55

Lapland55 48

Lapland64 55

Russia50 50

Russia41 50

Russia55 45

What is the value of the sample test statistic? (Round your answer to three decimal places.)